The nature of the specific heat peaks in kagome artificial spin ice is described in detail in the papers [1]}, [2]}. According to these works, there are four states of kagome artificial spin ice, and they can be clearly understood using dumbbell magnetostatic charge model. At high temperatures, artificial spin ice is in paramagnetic state, where all states are realized. As the temperature decreases, the highest energy states (in charge notation, these are vertices with charge \(\pm 3\) ) begin to disappear, and the transition from the paramagnetic state to the “Spin Ice I” state occurs. In Spin Ice I state the charge of each lattice vertex is either “\(+\) ” or “\(-\) ” but they are located chaotically on the lattice, and there are no vertices with charge “\(\pm 3\) ” left. The high-temperature peak of specific heat (at \(\approx \)  3.5 \(k_BT/D\) ) shows the transition of the system from the paramagnetic state to the Spin Ice I state. A further temperature decrease brings the system from Spin Ice I state to the Spin Ice II state, where charges of all vertices are ordered (each vertex with “\(+\) ” is adjacent to three vertices “\(-\) ” and vice versa). Such “crystallization” of vertex charges on the Kagome lattice gives the phase transition and the low-temperature peak of specific heat (at \(\approx \)  0.4 \(k_BT/D\) ). Eventually, the system comes to “Long-Range Order” state, where hexagons start to behave like meshing gearwheels.
